Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C67 ⋊ #3222 |
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,67|a^2=g,b^2=e,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,h^a=h^66,c^b=ce,d^b=dg,f^c=fg752 conjugacy classes — view the full character table.
| maximal subgroup of | #30776225, #30776228, #30776240, … |
| maximal normal subgroup of | #30776225, #30776228, #30776240, … |
| maximal quotient of | #30865205, #30865629, #30866421, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 15582);